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      Simplifying multiplication and division using multiples of 10

      I can factorise multiples of 10^n in order to simplify multiplication and division of both integers and decimals.

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      Lesson 10 of 17
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      • Year 7

      Simplifying multiplication and division using multiples of 10

      I can factorise multiples of 10^n in order to simplify multiplication and division of both integers and decimals.

      Lesson details

      Key learning points

      1. Factorising multiples of 10 can scale the calculation to easier values.
      2. It is important to consider place value so answers are scaled back correctly when multiplying.
      3. Factorising multiples of 10 is one of the multiplication and division strategies.

      Keywords

      • Product - A product is the result of two or more numbers multiplied together.

      • Partitioning - Partitioning is the act of splitting an object or value down into smaller parts.

      Common misconception

      That 0.0004 is one thousand times smaller than 4 as there are three zeros after the decimal point.

      The use of a place value or Gattegno chart is invaluable here to highlight this misconception . The 4 is in the 10 thousandths column.

      Challenge pupils to come up with their own products which are less than, equal to and larger than 24 using digits other than 4 and 6 which are used in the example.
      Teacher tip

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

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      6 Questions

      Q1.
      Select all the calculations which have a negative answer.

      Correct answer: $$(-37)\times92$$
      $$(-37)\times(-92)$$
      Correct answer: $$(-92)\times37$$
      $$(-92)\times(-37)$$

      Q2.
      Work out: $$(-4)\times(-6)=$$

      Correct Answer: 24

      Q3.
      Match each multiplication to the correct product.

      Correct Answer:$$3\times(-8)$$,$$(-24)$$
      Correct Answer:$$(-6)\times2$$,$$(-12)$$
      Correct Answer:$$(-6)\times(-6)$$,$$36$$
      Correct Answer:$$(-6)\times(-4)$$,$$24$$
      Correct Answer:$$(-6)\times6$$,$$(-36)$$
      Correct Answer:$$(-6)\times(-2)$$,$$12$$

      Q4.
      Work out: $$(-35)\div(-7)=$$

      Correct Answer: 5, five, Five

      Q5.
      Select all the correct statements.

      $$4\times(-5)\times(-2)=(-40)$$
      Correct answer: $$(-4)\times5\times(-2)=40$$
      Correct answer: $$4\times(-5)\times2=(-40)$$
      $$(-4)\times(-5)\times2=(-40)$$
      Correct answer: $$(-4)\times(-5)\times(-2)=(-40)$$

      Q6.
      Work out: $$(-100)\div5\div(-2)\div(-5)=$$

      Correct Answer: (-2), -2

      Assessment exit quiz

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      6 Questions

      Q1.
      ÷ 10 and × 10 are of each other.

      Correct Answer: inverses

      Q2.
      Complete the statement. Dividing by 10 is equivalent to multiplying by .

      Correct Answer: 0.1, 0.10

      Q3.
      Given that the product of 3 and 5 is 15, complete the statement. The product of 0.003 and 500 is __________ 15.

      Correct answer: less than
      equal to
      greater than

      Q4.
      Which of the following calculations have the decimal point in the correct place?

      Correct answer: 3.5 × 11.8 = 41.3
      35 × 1.18 = 4.13
      0.35 × 1.18 = 4.13
      Correct answer: 3.5 × 1.18 = 4.13

      Q5.
      Use the multiples of $$10^n$$ to work out $$40\;000 \times 0.002=$$

      Correct Answer: 80

      Q6.
      Use the multiples of $$10^n$$ to work out $$480\;000 \div 1600 = $$

      Correct Answer: 300

      Lesson appears in

      UnitMaths / Arithmetic procedures with integers and decimals

      Maths

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